We deal with weighted Hardy–Sobolev type inequalities for functions on ℝd, d ≥ 2. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish necessary and sufficient conditions for validity of these inequalities, and investigate the existence/nonexistence of extremal functions.
Cora, G., Musina, R., Nazarov, A. (2026). Hardy–Sobolev inequalities involving mixed radially and cylindrically symmetric weights. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS [10.1142/S0219199726500306].
Hardy–Sobolev inequalities involving mixed radially and cylindrically symmetric weights
Cora, G;
2026
Abstract
We deal with weighted Hardy–Sobolev type inequalities for functions on ℝd, d ≥ 2. The weights involved are anisotropic, given by products of powers of the distance to the origin and to a nontrivial subspace. We establish necessary and sufficient conditions for validity of these inequalities, and investigate the existence/nonexistence of extremal functions.
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